The present invention relates to a method and apparatus, together with an optical system, for measuring the diameter, distribution and so forth of micro liquid droplets and micro gas bubbles. More particularly, the present invention relates to a method and apparatus, together with an optical system, for simultaneously measuring the diameter and distribution of micro liquid droplets and micro gas bubbles distributed in a space by an interferometric method.
A method of accurately measuring the distribution and diameters of micro liquid droplets of fuel injected into an engine, for example, is demanded. Similarly, a method of accurately measuring the distribution and diameters of micro liquid droplets sprayed in the air is demanded to design a nozzle used in the spray dry method, for example. Further, a method of accurately measuring the diameter and distribution of gas bubbles, together with changes thereof, is demanded in the study of absorption of CO2 in air bubbles into the sea and the behavior of gas bubbles in beer and wine.
Thus, there is a strong demand in various fields for a method and apparatus for accurately measuring the diameter and distribution of micro liquid droplets and gas bubbles in the state of being present in a space.
Regarding micro liquid droplets, there has heretofore been a method in which micro liquid droplets distributed in a space are photographed and the photograph is analyzed. This method involves a problem in terms of measurement accuracy because the photograph may be out of focus or may become unsharp for other reasons. The method further suffers from the problem that real-time processing cannot be performed. A method in which the photograph is taken with a CCD camera is also known. This method also suffers from the problem in terms of measurement accuracy and the problem that real-time processing cannot be performed. Further, the method involves the problem that a great deal of time is required for analysis. A holographic technique and a method using a CCD camera for imaging are also known. However, these methods similarly involve the problem in terms of measurement accuracy and the problems that real-time processing cannot be performed and a great deal of time is required for analysis. There is also known a method in which the shadows of micro liquid droplets are captured directly with a CCD camera in order to obtain real-time capability. With this method, however, it is difficult to measure small particles because of the influence of diffraction. The method further involves the problem that it is difficult to measure the diameter of micro liquid droplets in limited three-dimensional positions.
In addition, there has heretofore been known a method in which a plurality of particles are simultaneously measured by specifying positions in a three-dimensional space with a method known as LDV, PDA, PDPA, etc. With this method, two laser beams are crossed in the air to form spatial interference fringes, and light scattered from liquid droplets crossing the interference fringes is observed with the same measurement volume from a plurality of different points. The diameters of the micro liquid droplets are measured from the phase differences between the measurement signals. In this case, because the diameter of each individual particle passing through the interference fringe area is measured, the method suffers from the problem that measurement in the space surrounding the interference fringe area cannot simultaneously be performed. The measurement accuracy is also unsatisfactory.
Under these circumstances, a method has been proposed (SAE Paper no. 950457, 960830) in which a sheet-shaped parallel laser beam is applied to a measurement space, and out-of-focus images of micro liquid droplets irradiated with the laser beam are captured. In the out-of-focus image corresponding to each micro liquid droplet, interference fringes are present, and there is a fixed relationship between the number of interference fringes present in the out-of-focus image and the diameter of the micro liquid droplet. Accordingly, the diameter of the micro liquid droplet can be measured by measuring the number of interference fringes. It is also possible to measure the spatial distribution of the micro liquid droplets.
With the above-described method of measuring the diameter and spatial distribution of micro liquid droplets by measuring the number of interference fringes in each out-of-focus image, the applicable field is limited to micro liquid droplets. The method has not heretofore been applied to micro gas bubbles.
Further, the above-described method involves the problem that when the spatial distribution density of micro liquid droplets is high, out-of-focus images overlap each other because they are circular and occupy large areas. Therefore, it is difficult to measure the diameters of the micro liquid droplets separately.
The present invention was made in view of the above-described problems with the prior art, and an object of the present invention is to expand the method of measuring the diameter and spatial distribution of micro liquid droplets by measuring the diameter of each out-of-focus image obtained by defocusing and the number of interference fringes in the out-of-focus image into a method of measuring the diameter and spatial distribution of micro gas bubbles, and to provide a measuring optical system that allows the method to be applied to a case where the spatial distribution density of micro liquid droplets and micro gas bubbles is high.
Another object of the present invention is to provide a method and apparatus for determining the position, diameter and velocity of micro liquid droplets and micro gas bubbles from the analysis of out-of-focus images.
A method of measuring the diameter, distribution and so forth of micro gas bubbles according to the present invention, which is provided to attain the above-described objects, is a method wherein a sheet-shaped parallel laser beam is applied to a liquid space in which micro gas bubbles are floating, and out-of-focus images of micro gas bubbles irradiated with the laser beam are captured from a lateral direction which is at an angle xcex8 to the direction of travel of the laser beam. The number N of interference fringes in the out-of-focus image corresponding to each micro gas bubble is measured, and the diameter D of the micro gas bubble is determined from the following relationship:
D=(2xcexN/nxcex1)[cos(xcex8/2)xe2x88x92sin(xcex8/2)÷{square root over ( )}{n2+1xe2x88x922n cos(xcex8/2)}]xe2x88x921xe2x80x83xe2x80x83(4) 
where xcex is the wavelength of the laser beam; xcex1 is the angle subtended at the micro gas bubble by an objective lens used to capture the image of the micro gas bubble; and n is the relative index of refraction of a liquid in which the micro gas bubble is present.
Another method of measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention is a method wherein a sheet-shaped parallel laser beam is applied to a space in which micro gas bubbles or micro liquid droplets are floating; out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam are captured from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam; and the numbers of interference fringes in the respective out-of-focus images corresponding to the micro gas bubbles or the micro liquid droplets are measured to determine the diameters and distribution of the micro gas bubbles or the micro liquid droplets.
The method is characterized in that the out-of-focus images are captured with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of the sheet-shaped parallel laser beam and an optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane.
In this case, it is desirable that the spacing of interference fringes on the imaging plane be adjustable by adjusting the defocus condition of the out-of-focus images.
The arrangement may be such that the sheet-shaped parallel laser beam is moved in parallel to a direction perpendicular to the plane of the sheet-shaped parallel laser beam with respect to the space in which micro gas bubbles or micro liquid droplets are floating, and the out-of-focus images are captured in synchronism with the movement of the sheet-shaped parallel laser beam.
Another method of measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention is a method wherein a sheet-shaped parallel laser beam is applied to a space in which micro gas bubbles or micro liquid droplets are floating, and linear out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam are captured from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of the laser beam and an optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane. The linear out-of-focus images extend in the direction of the plane in correspondence to the micro gas bubbles or the micro liquid droplets. The center of each of the out-of-focus images is determined to thereby determine the center position of the corresponding micro gas bubble or micro liquid droplet.
In this case, it is desirable that the center position be determined from a peak position of a moving average value obtained by taking an average in the range extending from a distance L/2 forward of a specific position to a distance L/2 rearward of the specific position in the longitudinal direction and determining the average to be a value at this position, where L is the length of a linear out-of-focus image, and successively moving the specific position.
Another method of measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention is a method wherein a sheet-shaped parallel laser beam is applied to a space in which micro gas bubbles or micro liquid droplets are floating, and linear out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam are captured from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of the laser beam and an optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane. The linear out-of-focus images extend in the direction of the plane in correspondence to the micro gas bubbles or the micro liquid droplets. Each of the out-of-focus images is subjected to Fourier transform to obtain a frequency, and the obtained frequency is multiplied by the length of the out-of-focus image to obtain the number of interference fringes in the out-of-focus image. The diameter of the micro gas bubble or the micro liquid droplet is determined on the basis of the number of interference fringes.
In this case, it is desirable that discrete Fourier transform be performed as the Fourier transform to obtain a discrete frequency distribution, and function fitting be applied to the discrete frequency distribution to obtain the diameter of the micro gas bubble or the micro liquid droplet.
A further method of measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention is a method wherein a sheet-shaped parallel laser beam is applied to a space in which micro gas bubbles or micro liquid droplets are floating, and two image frames are captured at a micro time interval xcex94t, each of which two image frames contains linear out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam. The linear out-of-focus images are captured from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of the laser beam and an optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane. The linear out-of-focus images extend in the direction of the plane in correspondence to the micro gas bubbles or the micro liquid droplets. Cross correlation between the two captured image frames is calculated for each linear out-of-focus image in the two captured image frames to obtain the displacement xcex94si of each linear out-of-focus image, and the velocity ui of each micro gas bubble or micro liquid droplet is determined from the following relationship:
ui=xcex94si/xcex94txe2x80x83xe2x80x83(6) 
In this case, it is desirable to remove a high-frequency component corresponding to interference fringes in the linear out-of-focus image when calculating cross correlation between the two captured image frames.
A still further method of measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention is a method wherein a sheet-shaped parallel laser beam is applied to a space in which micro gas bubbles or micro liquid droplets are floating, and linear out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam are captured from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of the laser beam and an optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane. The linear out-of-focus images extend in the direction of the plane in correspondence to the micro gas bubbles or the micro liquid droplets. The center of each of the out-of-focus images is determined to thereby determine the center position of the corresponding micro gas bubble or micro liquid droplet. Each of the out-of-focus images is subjected to Fourier transform to obtain a frequency, and the obtained frequency is multiplied by the length of the out-of-focus image to obtain the number of interference fringes in the out-of-focus image. The diameter of the micro gas bubble or the micro liquid droplet is determined on the basis of the number of interference fringes. Further, two image frames containing the linear out-of-focus images are captured at a micro time interval xcex94t. Cross correlation between the two captured image frames is calculated for each linear out-of-focus image in the two captured image frames to obtain the displacement xcex94si of each linear out-of-focus image, and the velocity ui of each micro gas bubble or micro liquid droplet is determined from the following relationship:
ui=xcex94si/xcex94txe2x80x83xe2x80x83(6) 
An apparatus for measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention includes laser beam application means for applying a sheet-shaped parallel laser beam to a space in which micro gas bubbles or micro liquid droplets are floating, and imaging means for capturing linear out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam, which is applied by the laser beam application means, from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of the laser beam and an optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane. The linear out-of-focus images extend in the direction of the plane in correspondence to the micro gas bubbles or the micro liquid droplets. The apparatus further includes center position measuring means for determining the center of each of the out-of-focus images to thereby determine the center position of the corresponding micro gas bubble or micro liquid droplet, and diameter measuring means for subjecting each of the out-of-focus images to Fourier transform to obtain a frequency, multiplying the obtained frequency by the length of the out-of-focus image to obtain the number of interference fringes in the out-of-focus image, and determining the diameter of the micro gas bubble or the micro liquid droplet on the basis of the number of interference fringes. Further, the apparatus includes velocity measuring means for capturing two image frames containing the linear out-of-focus images at a micro time interval xcex94t, calculating cross correlation between the two captured image frames for each linear out-of-focus image in the two captured image frames to obtain the displacement xcex94si of each linear out-of-focus image, and determining the velocity ui of each micro gas bubble or micro liquid droplet from the following relationship:
ui=xcex94si/xcex94txe2x80x83xe2x80x83(6) 
An optical system for measuring the diameter, distribution and so forth of micro gas bubbles and micro liquid droplets according to the present invention is a measuring optical system wherein a sheet-shaped parallel laser beam is applied to a space in which micro gas bubbles or micro liquid droplets are floating; out-of-focus images of micro gas bubbles or micro liquid droplets irradiated with the laser beam are captured from a lateral direction which is at a predetermined angle to the direction of travel of the laser beam; and the numbers of interference fringes in the respective out-of-focus images corresponding to the micro gas bubbles or the micro liquid droplets are measured to determine the diameters and distribution of the micro gas bubbles or the micro liquid droplets.
The measuring optical system is characterized by including an imaging optical system in which the focal length or the image-side principal plane in a direction parallel to a plane containing the direction of travel of the sheet-shaped parallel laser beam and an optical axis of the imaging optical system and the focal length or the image-side principal plane in a direction perpendicular to the plane containing the optical axis of the imaging optical system are different from each other, and image pickup means placed in an image plane which is in the vicinity of the image-formation plane in the direction perpendicular to the above-described plane and which is off the image-formation plane in the direction parallel to the above-described plane.
In this case, it is desirable that the imaging optical system be an anamorphic optical system comprising a combination of an axially symmetric objective lens and a cylindrical lens.
It is also desirable that at least one of the focal length and the image-side principal plane of the imaging optical system in the direction parallel to the plane be adjustable.
It is also desirable that the imaging optical system have a rectangular aperture elongated in the direction parallel to the plane.
In the present invention, out-of-focus images of micro gas bubbles or micro liquid droplets are captured with an imaging optical system at an imaging plane where the images are out of focus in a direction parallel to a plane containing the direction of travel of a sheet-shaped parallel laser beam and the optical axis of the imaging optical system and where the images are substantially in focus in a direction perpendicular to the plane. Consequently, the out-of-focus image corresponding to each micro gas bubble or micro liquid droplet becomes a one-dimensional image compressed in the direction perpendicular to the plane. Therefore, even when the spatial distribution density of micro gas bubbles and micro liquid droplets is high, the respective out-of-focus images can be separated from each other. Accordingly, the number of interference fringes in each out-of-focus image can be readily counted separately from each other. In addition, it becomes easy to determine the center position of each out-of-focus image to detect the distributed conditions of micro gas bubbles or micro liquid droplets. Even in such a case, the position, diameter and velocity distributions of micro gas bubbles and micro liquid droplets can be measured simultaneously and accurately.